Jesus rebukes the Pharisees for breaking God's law by adding to it. Pietists can't see the great danger in adding your own rules above and beyond the Bible, to make sure you don't disobey the Bible. True piety judges - and is judged - by what comes out of you, not by externals like what you see, eat or touch. We ought to be wise and careful - not doing fast food every day, not taking a 5 year old to an R movie, etc - but such wisdom is barely the beginning of piety.
After most confrontations with the Sadducees, headquartered in Jerusalem, Jesus withdraws to Galilee. After this confrontation with the Pharisees, dominant in Galilee, Jesus withdraws farther north, to Tyre and Sidon. He is not there to minister, yet He does. There is a difference between Jew and Gentile. The Son of David is for Israel, but if crumbs fall to the Gentiles and they have faith, that is all the more conviction for Israelites rejecting the bread on the table. Later, the apostles are sent to the ends of the earth, typically still to the Jew first, but also intentionally targeting the Gentiles.
To make the point stronger, Jesus feeds 4000 on the gentile side of the sea of Galilee. He is bread for Gentiles, too. He heals a Gentile, so he can hear and speak, while shaking His head at deaf and mute Israel.